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<H1>Measurement of Upsilon(1S) Polarization</H1>

<p>This web page provides a summary of the measurement of polarization of Upsilon(1S) mesons.  This measurement provides a test for NRQCD, which predicts a transverse polarization at high pT.</p>

<p>This measurement was performed using 2.9 fb<sup>-1</sup> of data.  We utilize a template method wherein fully transverse and fully longitudinal Monte Carlo samples are generated and subjected to detector acceptance and efficiency effects to form templates.  Monte Carlo is iteratively re-weighted to match data pT distributions.  Based on the shapes of the polar angle distributions of the positive muon in the s-channel helicity frame, we determine a polarization parameter by matching a polarization-weighted combination of templates to data in each of eight Upsilon pT bins.  Events are selected using a mass fit, and backgrounds are evaluated using mass sidebands.</p>

<p>We find that the Upsilons are unpolarized at low pT before developing strongly-transverse characteristics at high-pT, in contrast with the NRQCD prediction.  The results are shown below, represented by the parameter alpha which has possible values ranging from -1 (fully longitudinal) to 1 (fully transverse).  The parameter eta in the table is the fraction of longitudinally-polarized events.</p>

<p>The analysis is discussed in detail in <a href="cdf9966_ups_1s_pol_public.pdf">CDF public note 9966</a>.</p>

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<H2>Blessed plots for Y(1S) Polarization Analysis</H2>

<p>Figure 1: Mass histogram showing all three Upsilon peaks and their separation. (<A href="blessedplots/massfits_allpeaks.eps">eps</A>), (<A href="blessedplots/massfits_allpeaks.jpg">jpg</A>)
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Figure 2: Mass histograms for Y(1S) in pT bins including fits from which the exponential background shapes were determined. (<A href="blessedplots/massfits_expBG.eps">eps</A>), (<A href="blessedplots/massfits_expBG.jpg">jpg</A>)
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Figure 3: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the first Y(1S) pT bin (2-3 GeV/c). (<A href="blessedplots/upsi1S_pt1_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt1_fit.jpg">jpg</A>)
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Figure 4: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the second Y(1S) pT bin (3-4 GeV/c). (<A href="blessedplots/upsi1S_pt2_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt2_fit.jpg">jpg</A>)
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Figure 5: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the third Y(1S) pT bin (4-6 GeV/c). (<A href="blessedplots/upsi1S_pt3_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt3_fit.jpg">jpg</A>)
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Figure 6: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the fourth Y(1S) pT bin (6-8 GeV/c). (<A href="blessedplots/upsi1S_pt4_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt4_fit.jpg">jpg</A>)
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Figure 7: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the fifth Y(1S) pT bin (8-12 GeV/c). (<A href="blessedplots/upsi1S_pt5_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt5_fit.jpg">jpg</A>)
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Figure 8: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the sixth Y(1S) pT bin (12-17 GeV/c). (<A href="blessedplots/upsi1S_pt6_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt6_fit.jpg">jpg</A>)
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Figure 9: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the seventh Y(1S) pT bin (17-23 GeV/c). (<A href="blessedplots/upsi1S_pt7_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt7_fit.jpg">jpg</A>)
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Figure 10: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the eighth Y(1S) pT bin (23-40 GeV/c). (<A href="blessedplots/upsi1S_pt8_fit.eps">eps</A>), (<A href="blessedplots/upsi1S_pt8_fit.jpg">jpg</A>)
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Figure 11: Measured polarizations (alpha) compared with D0 results (from PRL 101 182004). (<A href="blessedplots/Y1s_Alpha_d0comp.eps">eps</A>), (<A href="blessedplots/Y1s_Alpha_d0comp.jpg">jpg</A>)
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Figure 12: Measured polarizations (alpha) compared with CDF Run I results (from PRL 88 161802). (<A href="blessedplots/Y1s_Alpha_run1comp.eps">eps</A>), (<A href="blessedplots/Y1s_Alpha_run1comp.jpg">jpg</A>)
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Figure 13: Measured polarizations (alpha) compared with NRQCD predictions (from Braaten & Lee, PRD 63 071501).(<A href="blessedplots/Y1S_alpha_withNRQCD.eps">eps</A>), (<A href="blessedplots/Y1S_alpha_withNRQCD.jpg">jpg</A>)
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Figure 14: Table of results. (<A href="blessedplots/results_table.ps">ps</A>), (<A href="blessedplots/results_table.jpg">jpg</A>)
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Figure 15: Y(1S) background cos(theta*) distributions in each pT bin. (<A href="blessedplots/Y1S_bg.eps">eps</A>), (<A href="blessedplots/Y1S_bg.jpg">jpg</A>)</p>
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